We were given problems to work out before asked the meaning, but I have done them and am pretty confident with the answers, however I do not know the meaning of what I calculated. Please let me know if you need the entire problem to do this, although I think you can give me an idea of what I calculated for each.
Explain the meaning of what we are calculating for the following;
Integral with Respect to Surface Area:
- My attempt: Clueless
Surface Integral
- My attempt: Measured the flux of a vector field across surface area?
Stoke’s Theorem
- My attempt: Stokes theorem is Green’s theorem with essentially two small changes. Changing the line integral to 3 dimensions and the double integral to a surface integral F.n(ie floating in space). So basically we calculated an area of a surface in 3 dimensional region using stokes theorem.
Divergence Theorem
- My attempt: By using the divergence theorem we calculated a result that relates the flow the flux of a vector field through a surface to the behavior of the vector field inside the surface. Overall, what we calculated is the net flow out of a particular region which was defined by the problem given.
Help extremely appreciated, thank you!